Plane quartics containing the ten vertices of a complete pentalateral and limits of them are called Lüroth quartics. The locus of singular Lüroth quartics has two irreducible components, both of codimension two in P14. We compute the degree of them and discuss the consequences of this computation on the explicit form of the Lüroth invariant. One important tool is the Cremona hexahedral equations of the cubic surface. We also compute the class in M̄3 of the closure of the locus of nonsingular Lüroth quartics.
Ottaviani, G., Sernesi, E. (2011). On singular Luroth quartics. SCIENCE CHINA. MATHEMATICS, 54(8), 1757-1766 [10.1007/s11425-010-4123-3].
On singular Luroth quartics
SERNESI, Edoardo
2011-01-01
Abstract
Plane quartics containing the ten vertices of a complete pentalateral and limits of them are called Lüroth quartics. The locus of singular Lüroth quartics has two irreducible components, both of codimension two in P14. We compute the degree of them and discuss the consequences of this computation on the explicit form of the Lüroth invariant. One important tool is the Cremona hexahedral equations of the cubic surface. We also compute the class in M̄3 of the closure of the locus of nonsingular Lüroth quartics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
